[tex]\bf ~~~~~~~~~~~~\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
\qquad \qquad
\cfrac{1}{a^n}\implies a^{-n}
\qquad \qquad
a^n\implies \cfrac{1}{a^{-n}}
\\\\
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\left( \cfrac{t^4}{10y^4} \right)^{-4}\implies \left( \cfrac{10y^4}{t^4} \right)^{4}\impliedby \textit{then we distribute the exponent}
\\\\\\
\left( \cfrac{10^4y^{4\cdot 4}}{t^{4\cdot 4}} \right)\implies \cfrac{10000y^{16}}{t^{16}}[/tex]
